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There are two parts to this. First is, "What is the physical significance of a wave function?" Secondly, "Why do we normalize it?"

To address the first:
In the Wave Formulation of quantum mechanics the wave function describes the state of a system by way of probabilities. Within a wave function all 'knowable' (observable) information is contained, (e.g. position (x), momentum (p), energy (E), ...). Connected to each observable there is a corresponding operator [for momentum: p=-i(hbar)(d/dx)]. When the operator operates onto the wave function it extracts the desired information from it. This information is called the eigenvalue of the observable... This can get lengthy so I'll just leave it there. For more information I suggest reading David Griffith's "Introduction to Quantum Mechanics". A math knowledge of Calculus II should suffice.

To address the second:
Normalization is simply a tool such that since the probability of finding a particle in the range of +/- (infinity) is 100% then by normalizing the wave function we get rid of the terms that muddy up the answer the probability.
An un-normalized wave function is perfectly fine. It has only been adopted by convention to normalize a wave function.

ex. un-normalized wave function (psi is defined as my wave function)
- The integral from minus infinity to positive infinity of |psi|^2 dx = 2pi

ex. normalized wavefunction
- The integral from minus infinity to positive infinity of |psi|^2 dx = 1

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Verla Becker

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How can you derive wave function?

The wave function in quantum mechanics is derived by solving the Schrödinger equation for a given physical system. The Schrödinger equation describes how the wave function evolves in time, and its solution provides information about the quantum state of the system. Different boundary conditions and potentials will lead to different wave functions.


Why hydrogen has special significance in quantum mechanics?

Hydrogen is special in quantum mechanics because its simplest form, the hydrogen atom, is the only atom for which the Schrödinger equation can be solved analytically. This allows for detailed insight into the behavior of electrons in the atom, providing a fundamental understanding of quantum mechanics. Additionally, hydrogen plays a key role in the development of quantum theories and helps explain important phenomena such as emission spectra and energy levels in atoms.


What is the Alternative to the Quantum Mechanics theory?

There is no reasonable alternative to quantum mechanics, at least not something that can even compare with the predictive power and experimental accuracy as quantum theory. If you want to make predictions about things happening at small scales you cannot do without quantum mechanics. Also note that certain models which are now considered as possible theories of everything (e.g. string theory) all expand upon quantum mechanics, they do not make quantum mechanics invalid or unnecessary.


What are the postulates of wave mechanics?

The postulates of wave mechanics are: The state of a quantum system is described by a wave function. The wave function evolves over time according to the Schrödinger equation. Physical observables are represented by Hermitian operators, with measurement outcomes corresponding to eigenvalues of these operators. Measurement collapses the wave function to one of the eigenstates of the observable being measured.


Who is the founder of quantum mechanism?

Quantum mechanics was developed by multiple scientists in the early 20th century, including Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, and Erwin Schrödinger. There is no single founder of quantum mechanics as it was a collaborative effort by several physicists.

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